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I don't play so much anymore but used to play a lot of tournaments and was rated around 1800...not great, not bad.

If I was to teach someone, I would start with an endgame book. There are several out there that are very good. You can probably go to a used bookstore and pick one inexpensively or just use Amazon. Many players can get through the opening and be very creative in the middlegame but are lost once it's down to Kings and pawns. If one becomes very fluent with how to win in the endgame, that person can just play defensively and trade off pieces until voila! just Kings pawns and minor pieces are left. This is where the isolated pawns are exploited and Queens are born. Most computer chess programs can be manually set up so that you can practice endgame strategies. This will seem like drudgery but will yield great benefits for the entire time you play chess.

Next, would be the opening. I would recommend knowing one opening cold as white (either e4 or d4) and know how to counteract the basic defenses to it. As black you will need to know two defenses against e4, the other against d4. If white starts out with, say g3 or Nf3 or Nc3, you can usually maneuver it back to one of your known defenses. If white starts out with say h4, they either don't know what they are doing or are being a smart ass, either way it just makes it easier to control the center. I would suggest Modern Chess Openings (MCO) as the first book to buy. Computers are great learning tools for the openings, their library is quite extensive.

Next is the favorite. You will never get an advantage against a computer in the opening or endgame. Your only hope is in the middlegame where the creativity of the player is matched against the deep calculating ability of the computer. If you subscribe to the USCF, you get Chess Life sent to your house monthly. It's a great tool for the beginner. Anyway, playing the games of the grandmasters will maybe help you find a player or two whose style makes a lot of sense to you. For me it was Fischer and Kasparov ( not suggesting I play at that was more of a "recognizing the correct answer when told" kind of thing). Some players build an impenetrable fortress, others sacrifice for the attack...just find what suits your style and then study those players.

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